Concept 3 of 7
Add It Up: Carrying Big Numbers
Today's big idea
A column can only hold one digit, so anything over 9 sends a ten next door.
Ten ones bundle into a single ten, which is why the little 1 moves left.
How it works
👀 What's going on?
Adding 5 + 3 is easy, and you do it without thinking. Now try 3,748 + 2,675. Four columns at once will not stay in your head. So you take one column at a time, and deal with the mess when a column fills up.
💡 Here's the trick
Look at the stack above. A column can only hold one digit, 0 to 9. When a column adds past 9 you write down the ones part and send the ten next door to the left. That is allowed because ten ones really are one ten, ten tens really are one hundred, and ten hundreds really are one thousand.
🪄 How to do it
- 1.Stack the numbers so the columns line up, the way the sum above lines them up.
- 2.Add the ones. If the total passes 9, write the ones digit and carry the ten left.
- 3.Move left one column at a time, adding the carry in each time you land.
✍️ Try it
Work out 3,748 + 2,675. Then try 4,092 + 986, where one column starts on a 0.
For the first, ones give 13, so write 3 and carry 1. Tens give 4 + 7 + 1 = 12, so write 2 and carry 1. Hundreds give 7 + 6 + 1 = 14, so write 4 and carry 1. Thousands give 3 + 2 + 1 = 6, making 6,423. For the second, the tens give 9 + 8 = 17, so write 7 and carry 1, then the hundreds give 0 + 9 + 1 = 10, so write 0 and carry again, giving 5,078.
⚠️ Watch out
You might be thinking the carried 1 is just a reminder scribble. It is a real ten, and it has to be added in. Forget it in 3,748 + 2,675 and the tens give 11 instead of 12. The answer comes out 6,413, with only one digit looking wrong.
🌟 Why this matters
Every bill, every score and every distance you ever add is this, just with bigger numbers. Getting it steady now means never having to think about it again.
Exam tip: Most lost marks here are a dropped carry, not a wrong fact, so check the carries first.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Add: 256 + 178”
- 1
Stack and start at ones
Line up: 256 on top, 178 below. Ones: 6 + 8 = 14.
- 2
Write 4, carry the 1
Write the 4 in ones. Carry the 1 to the tens column. 🚚
- 3
Tens column
1 (carry) + 5 + 7 = 13. Write 3, carry 1 to hundreds.
- 4
Hundreds + carry ✓
1 + 2 + 1 = 4. 256 + 178 = 434
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Blue rods are tens, yellow squares are ones. Pile the ones, and when you get 10 of them, trade 10 ones for 1 ten.
27 + 18
ROUND 1 OF 2Quick check
✅ VERIFICATION
When you add 6 + 8 in the ones column, the result is 14. What do you write in the ones column, and what do you carry to the tens?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Take It Away
Trade 1 ten for 10 ones when the column is short.